The electrical wiring in my house has two ages. Half the house has wiring from back in 1963 and the other half has wiring from 1986. Conveniently, my room runs on the older wiring. It's due for change but I'm gonna have to convince some people to allow me to get it done. My room runs on a 20A amp breaker and currently I have about 5-9A in use. I'm gonna be adding some equipment to the room which would bring the current usage up to 15A running 24/7. Would it be safe to say that this old af wiring would handle it or should I get an electrician to change my wiring one time?
If the wiring was done properly in 1963, it should be fine carrying 20A in 2020.
1963 is hardly the dark ages, electrically. A 12Ga copper circuit from that era, IF properly constructed (tight connections, etc.) does not need the wire changed from old age. If anything is likely to need to be changed from aging, it would be the receptacles, and that's not a "must do" but "if they appear to be loose or otherwise making poor connections, show any signs of soot, have broken plastic, or are abnormally warm in use, then change them." And if you change them, use quality receptacles and use the screw terminals to connect the wires.
Receptacle springs can and do age to the point where the receptacle contacts make poor connections to the plug contacts.
Backstabs (push-in backwire connections on outlets) are not rated for 12Ga wire (at least any I've seen) and in any case are a terrible system that should never have been approved. There are quality screw-clamped connections that appear similar to a backstab if you don't know the difference, but they are screwed to clamp, not poked in and held by a spring. Normal side screw connections with the wires curled around them (clockwise, please) are also fine.
If you happen to have 10 Ga Aluminum wire, check back, as there are some things to deal with differently there, and more concern if you don't, but your house is from a couple of years before that was common, so you probably have 12Ga copper, unless something was done wrong with wiring your 20A circuit.
As for the load level, you can run up to 80% of the breaker trip as a continuous (more than 3 hours at a time) load, so 16A on a 20A breaker. which means 15A continuous is fine.
Now, the other part that "might need changed" depending on what it is, specifically, 57 years on, would be the breaker panel. Certain panels are notorious for performing poorly, causing fires, or having breakers that fail to trip in an overload (and then cause fires.) Federal Pacific and Zinsco are two that spring to mind commonly, there may be others. Those are not so much "because you are planning to run a 15A continuous load" but "you are simply lucky that they have not burned your house down, yet" and every day is another opportunity for that to change. Other 57 year old panels and breakers may well be fine for another 50 years